. On, 11 -llA-t A(t(/)) -A-t.4(tr-)lt < ltl

I. C. André and M. Chipot, A remark on uniqueness for quasilinear elliptic equations. A paraitre dans les Proceedings du Banach Center. tB.l H. Brezis : Analyse fonctionnelle, théorie et application, 1983.

[. B. , J. M. Ball, and R. D. , James: Fine phase mixturcs as minimizers of energy-Arch, Rational Mech. Anal, vol.100, pp.13-52, 1987.

[. B. , J. M. Ball, and R. D. James, Proposed experimental tests of a theory of fine microstructures, Phil. Trans. Roy. Soc. London

J. M. Ml, F. Ball, and . Murat, IAt,p quasiconvexity and variational problems for multiples integrals, J. Funt. Anal, vol.58, pp.255-253, 1984.

B. Brighi, Sur quelques problèmes de calcul des Variations et I'approximation de leur fonctionnelle relaxé. Thesis, 1991.

[. B. Brighi and M. Chipot, Approximation in nonconvex problems, Proceedings of the first European Conference on Elliptic and Parabolic Problems, 1991.

P. G. Ciarlet, Plates and junctions in elastic multi-structures, An asymptotic analysis, 1990.

[. B. Brighi and M. Chipot, Approximaaed convex envelope of a function, SIAM J. of numerical Analysis

[. Chipot, Hyperelasticity for crystals, European Journal of Applied Mathematics, vol.64, issue.02, pp.3-129, 1990.
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[. Chipot, Energy estimates for variational problems with nonhomogeneous boundary conditions Nonlinear mathematical problems in industry, Gakuto International Series, Mathematical Sciences and Applications, vol.2, p.473487, 1993.

M. C. Références-bibliograph-iques-tc, C. Chipot, and . Collins, Numerical approximation in variational problems with poaential wells, SIAM J. of Numerical Analysis, vol.29, issue.4, p.473487, 1993.

M. C. Tc, C. Chipot, D. Collins, and . Kinderlehrer, Numerical analysis of oscillations in multiple well problems, Numerische Mathematik, vol.70, pp.259-282, 1995.

M. E. Tc, A. Chipot, and . Elfanni, On the numerical analysis of some variational problems with nonhomogeneous boundary.conditions

M. K. Tc, D. Chipot, and . Kindcrlehrer, Equilibriurn configurations of crystals, Arch. Rational Mech. Anal, vol.103, pp.237-277, 1988.

M. L. Tc, V. /. Chipot, and . Li, Variational prnblems with poaential wells and nonhomogeneous boundary conditions Calculus of variations, homogeniazation and continuum mechanics, Series on Advances in Mathematics for applied Sciences

. M. Tc, S. Chipot, and . Mûller, Sharp energy estimates to frnae element approximations for non-convex problems (to

. K. Co, D. Collins, M. Kinderlehrer, and . Luskin, Numerical approximation of the solution of a variational problem with a double well potential, SIAM J. Numer. Anal, vol.28, pp.321-332, 1991.

C. L. Co, M. Collins, and . Luskin, The computation of austenetic-martensitic phase transition In Partial Differencial Equations and Continum Models of Phase Transitions, Lecture Notes in Physics il 344, pp.34-50, 1989.

C. L. Co, M. Collins, and . Luskin, Computational results for phase transition in shape memory materials, smart Maaerials, Structure, and Mathematical Issues, pp.198-215, 1989.

C. L. Co, M. Collins, and . Luskin, Numerical modeling of the microstructure of crystals with symmetry-related variants, Proceedings of the ARO US-Japan Workshop on smart /Intelligent Maaerials

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[. Fonseca, The lower quasiconvex envelope of stored energy function for an elastic crystal, J. Math. Pures et App, vol.67, pp.175-195, 1988.

[. D. James, Basic principles for the improvement of shap-memory and relaaed materials, smart Materials, Structure, and Mathematical Issues, 1989.

[. D. James, Microstructure and weak convergence. ln Material Instabilities in Continum Mechanics and Related Problems, pp.75-196, 1987.

R. K. Tj, D. James, and . Kinderlehrer, Theory of diffusionless phase transitions In Partial Differencial Equations and Continum Models of Phase transitions., I-?cture Notes in Physics, pp.5-84, 1989.

. D. Kinderlehrer, Remarks about equilibrium configurations of crystals, Maaerial Instabilities in Continum Mechanics and, pp.217-242, 1987.

R. R. Ko and . Kohn, The relationship hetween linear and nonlinear variational models of coherent phase transitions, Proceedings of seventh Army Conference on applied Mathematics and Computing, 1993.

P. T. Tr, J. M. Raviart, and . Thomas, Introduction à I'analyse numérique des équations aux dérivées partielles, 1988.

. Anne, . Mesures, A. Young, and I. Mesures-de-young-soient-f-)-un-ouvert-bomé-de, rh : f) x IR---+ IR une fonction continue et une suite up ? (r On considère la suiae de fonctions l:(r,up(ae)) Si z1 converge vers u et t[(.,ur(.)) converge vers y'-, alors en gên&al t!' + tb(.,r(.)). [a notion de mesures de Young associée à u6 va nous perrnettre d'exprimer dl. Avant d'énoncer le théorème d'existence des mesures de Young, rappelons quelque.s résultats d'analyse fonctionnelle. L'espace co(IR,-): {.f e c(IR-) : r^tl, o} est un espace de Banach pour la nolme de la convergence uniforme. Son espace dual est I'espace des mesure.s de Radon noté ilr'(IR-) muni de la norme llPllnzrm-y: hl(R-)

P. Co and L. , IR-) est séparable on a : (lt(ç1

. Le, 1 tr,l; r: I tg@, IR-)) et p e trf.(C), l/(IR*)) où -Lf

. La-norme-dans-tff, il4(IR-)) est llpll : sup essr?ollp"llrrrIR-i

. Théorème, tls : f) x IR---IR, une fonction ile Carathéod,ory et u6: O -* IR-u,ne suite ile fonctions rnesurable-s tellc qu,e: l"r(')l <Cp.p. r?f)Vk